Karate (???) (Japanese pronunciation: [ka?ate] (Speaker Icon.svg listen), English: /k?'r?:ti:/) is a martial art developed in the Ryukyu Islands (Okinawa) from indigenous fighting methods te (?, literally: "hand"?) and Chinese kenp?.[1][2] Karate is characterised as a striking art using punching, kicking, knee and elbow strikes and open-handed techniques such as knife-hands (karate chop). Grappling, locks, restraints, throws, and vital point strikes are taught in some styles.[3]
Hapkido (also spelled hap ki do or hapki-do) is a dynamic and eclectic Korean martial art. It is a form of self-defense that employs joint locks, techniques of other martial arts, as well as common unskilled attacks. There is also the of use traditional weapons, including the short stick, cane, rope, nunchucku, sword, and staff which vary in emphasis depending on the particular tradition examined.
Hapkido contains both long and close range fighting techniques, utilizing dynamic kicking and percussive hand strikes at longer ranges and pressure point strikes, jointlocks, or throws at closer fighting distances. Hapkido emphasizes circular motion, non-resisting movements, and control of the opponent. Practitioners seek to gain advantage through footwork and body positioning to employ leverage, avoiding the use of strength against strength.
Karate originated on an island called Okinawa, which is a Japanese territory now. In the 1920's and 30's, it was taken to the main Japanese islands. There are a wide variety of "styles" of karate. Some emphasize long-range striking, some focus on close-range hooking and pulling techniques. Karate is, generally speaking, a striking art, meaning the main focus is on punches and kicks, and strikes with other weapons, such as the knee, elbow, wrist, or edge of the hand. Every karate style will have a series of "kata". Kata is both a singular and plural term; a kata is a collection of offensive and defensive sequences that look a bit like a dance. They are performed solo, although some schools will have two-person sequences. Sometimes, weapons are taught in karate, although these tend to be traditional Okinawan weapons and, if taught at all, are usually taught to those with a few years of experience.
Hapkido is a Korean martial art that has its roots in Japanese Jujitsu, the unarmed fighting system of the Samurai. It is known for having a wide variety of locks and holds, especially wrist locks, as well as throws and sweeps. Hapkido incorporates striking into its system, although this tends to be secondary to its grappling. It has a wide variety of unconventional kicks. Sometimes, weapons like sticks and swords will be used in training, but like karate, Hapkido is primarily an empty-hand system. Unlike karate, solo forms like kata are generally not taught.
Hapkido:
http://www.youtube.com/watch?v=CVTAWLJCdOY
http://www.youtube.com/watch?v=MnNMCpOqyV0
http://www.youtube.com/watch?v=VMBQZ8FWcE8
As to which is better for self-defense, that's really up to how good the individual instructor is and how good the student is. A lot of people are looking for the "best" martial art, but really, there's no magic bullet. I'd suggest attending classes in both, and going with your gut instinct on what makes you feel the most comfortable.
Karate is a predominantly striking martial art, originating on the Japanese island of Okinawa.
Hapkido is a Korean system. Its strikes owe a great deal to karate- but like all Korean karate systems, they focus slightly more heavily on kicks than on punching techniques. They also do in a good deal of grappling, which is quite uncommon in karate.
Because it covers two essential kinds of combat- striking and grappling- rather than just one, Hapkido will probably be a somewhat better idea for self-defense on the whole- but check out both schools if they're in your area, because instructor quality matters a lot more than the differences between arts.